About: Convergence to stationary solutions for a parabolic-hyperbolic phase-field system

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	A parabolic-hyperbolic nonconserved phase-field model is here analyzed. This is an evolution system consisting of a parabolic equation for the relative temperature .theta. which is nonlinearly coupled with a semilinear damped wave equation governing the order parameter .chi..The latter equation is characterized by a nonlinearity .fi.(.chi.) with cubic growth. Assuming homogeneous Dirichlet and Neumann boundary conditions for .theta. and .chi., we prove that any weak solution has an .omega.-limit set consisting of one point only. This is achieved by means of adapting a method based on the Łojasiewicz-Simon inequality. We also obtain an estimate of the decay rate to equilibrium. A parabolic-hyperbolic nonconserved phase-field model is here analyzed. This is an evolution system consisting of a parabolic equation for the relative temperature .theta. which is nonlinearly coupled with a semilinear damped wave equation governing the order parameter .chi..The latter equation is characterized by a nonlinearity .fi.(.chi.) with cubic growth. Assuming homogeneous Dirichlet and Neumann boundary conditions for .theta. and .chi., we prove that any weak solution has an .omega.-limit set consisting of one point only. This is achieved by means of adapting a method based on the Łojasiewicz-Simon inequality. We also obtain an estimate of the decay rate to equilibrium. (en) V práci je analyzován evoluční systém sestávající z parabolické rovnice pro teplotu nelineárně spojené se semilineární tlumenou vlnovou rovnicí pro fázovou proměnnou s kubickou nelinearitou. Za předpokladu homogenních Dirichletových podmínek pro teplotu a množinu sestávající z jediného stacionárního stavu a je odhadnuta rychlost konvergenve k tomuto bodu. Důkaz se opírá o modifikaci Łojasiewiczovy-Simonovy věty. (cs)
Title	Convergence to stationary solutions for a parabolic-hyperbolic phase-field system Convergence to stationary solutions for a parabolic-hyperbolic phase-field system (en) Konvergence ke stacionárním řešením pro parabolicko-hyperbolický systém fázového pole (cs)
skos:prefLabel	Convergence to stationary solutions for a parabolic-hyperbolic phase-field system Convergence to stationary solutions for a parabolic-hyperbolic phase-field system (en) Konvergence ke stacionárním řešením pro parabolicko-hyperbolický systém fázového pole (cs)
skos:notation	RIV/67985840:_____/06:00044581!RIV07-AV0-67985840
http://linked.open.../vavai/riv/strany	827;838
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(IAA1019302), Z(AV0Z10190503)
http://linked.open...iv/cisloPeriodika	4
http://linked.open...vai/riv/dodaniDat	2007
http://linked.open...aciTvurceVysledku	Petzeltová, Hana
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Matematický ústav AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	469807
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/06:00044581
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	phase-field models; convergence to stationary solutions; Łojasiewicz-Simon inequality (en)
http://linked.open.../riv/klicoveSlovo	phase-field models Łojasiewicz-Simon inequality convergence to stationary solutions
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[BA5B3D7C7C2F]
http://linked.open...i/riv/nazevZdroje	Communications on Pure and Applied Analysis
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Compatibility of dynamics and statics in multicomponent dissipative systems
http://linked.open...UplatneniVysledku	2006
http://linked.open...v/svazekPeriodika	5
http://linked.open...iv/tvurceVysledku	Petzeltová, Hana Schimperna, G. Grasselli, M.
http://linked.open...n/vavai/riv/zamer	Rozvoj a prohloubení obecných matematických poznatků a jejich užití v dalších vědních oborech a v praxi
issn	1534-0392
number of pages	12 (xsd:int)
is http://linked.open...avai/riv/vysledek of	Convergence to stationary solutions for a parabolic-hyperbolic phase-field system Convergence to stationary solutions for a parabolic-hyperbolic phase-field system

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